How do I get new Summoner icons?

The new summoner icons are to be unlocked via achievements. However, achievements haven’t yet been released in LOL (You’ll find the ‘not yet accessible’ tab in your summoner profile).

How do I get the new KDA icon?

With the rewards live from November 6, you’ll need to visit the League page on Twitch’s Prime Gaming website. Log in with a Twitch account that has an active Prime Gaming subscription. Once you log in, click the ‘Claim Now’ button next to the ‘ League of Legends: K/DA Icon Capsule’ reward.